Cosmological lower bound on the circuit complexity of a small problem in logic
暂无分享,去创建一个
[1] Albert R. Meyer,et al. WEAK MONADIC SECOND ORDER THEORY OF SUCCESSOR IS NOT ELEMENTARY-RECURSIVE , 1973 .
[2] G. J. Chaitin. The berry paradox , 1995 .
[3] Avi Wigderson,et al. P = BPP if E requires exponential circuits: derandomizing the XOR lemma , 1997, STOC '97.
[4] 守屋 悦朗,et al. J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .
[5] Paul E. Dunne,et al. The Complexity of Boolean Networks , 1988 .
[6] Eric Allender. Some Pointed Questions Concerning Asymptotic Lower Bounds, and News from the Isomorphism Front , 2001, Current Trends in Theoretical Computer Science.
[7] J. Hartmanis,et al. On the Computational Complexity of Algorithms , 1965 .
[8] I. Chuang,et al. Quantum Computation and Quantum Information: Bibliography , 2010 .
[9] Jr. Hartley Rogers. Theory of Recursive Functions and Effective Computability , 1969 .
[10] Richard J. Lipton,et al. Some connections between nonuniform and uniform complexity classes , 1980, STOC '80.
[11] Juris Hartmanis,et al. On Isomorphisms and Density of NP and Other Complete Sets , 1977, SIAM J. Comput..
[12] D. Deutsch. Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[13] A. Yao. Separating the polynomial-time hierarchy by oracles , 1985 .
[14] Stephen A. Cook,et al. The complexity of theorem-proving procedures , 1971, STOC.
[15] Andrzej Ehrenfeucht,et al. Practical Decidability , 1975, J. Comput. Syst. Sci..
[16] Leonard M. Adleman,et al. Two theorems on random polynomial time , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).
[17] Ingo Wegener,et al. The complexity of Boolean functions , 1987 .
[18] Ingo Wegener,et al. The Complexity of Symmetric Boolean Functions , 1987, Computation Theory and Logic.
[19] D. C. Cooper,et al. Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.
[20] Christopher B. Wilson. Relativized circuit complexity , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).
[21] Yehoshua Bar-Hillel,et al. The Intrinsic Computational Difficulty of Functions , 1969 .
[22] A. Paz. Probabilistic algorithms , 2003 .
[23] Donald E. Knuth. Selected papers on computer science , 1996, CSLI lecture notes series.
[24] J. Edmonds. Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.
[25] Yuri Gurevich,et al. Average Case Completeness , 1991, J. Comput. Syst. Sci..
[26] Walter L. Ruzzo. On Uniform Circuit Complexity , 1981, J. Comput. Syst. Sci..
[27] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .
[28] Frederik Pohl. Beyond the Blue Event Horizon , 1980 .
[29] Larry J. Stockmeyer,et al. The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..
[30] Andrew Chi-Chih Yao,et al. Separating the Polynomial-Time Hierarchy by Oracles (Preliminary Version) , 1985, FOCS.
[31] R. Impagliazzo,et al. P=BPP unless E has sub-exponential circuits: Derandomizing the XOR Lemma , 2002 .
[32] D E Knuth,et al. Mathematics and Computer Science: Coping with Finiteness , 1976, Science.
[33] Norbert Blum. A Boolean Function Requiring 3n Network Size , 1984, Theor. Comput. Sci..
[34] Michael A. Harrison,et al. Introduction to switching and automata theory , 1965 .
[35] Miklós Ajtai,et al. ∑11-Formulae on finite structures , 1983, Ann. Pure Appl. Log..
[36] Nicholas Pippenger,et al. On simultaneous resource bounds , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).
[37] M. Fischer,et al. SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC , 1974 .
[38] Michael Sipser,et al. Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).
[39] Umesh V. Vazirani,et al. Quantum complexity theory , 1993, STOC.
[40] Gregory J. Chaitin. The Berry paradox , 1995, Complex..
[41] John Gill,et al. Computational Complexity of Probabilistic Turing Machines , 1977, SIAM J. Comput..
[42] Michael A. Nielsen,et al. Quantum Computation and Quantum Information Theory , 2000 .
[43] Ming Li,et al. Kolmogorov Complexity and its Applications , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.
[44] Miklós Ajtai,et al. Generating Hard Instances of Lattice Problems , 1996, Electron. Colloquium Comput. Complex..
[45] A. R. Meyer,et al. COMPUTATIONALLY COMPLEX AND PSEUDO-RANDOM ZERO-ONE VALUED FUNCTIONS††Portions of this work were carried out at Carngie-Mellon University, while the authors were in the Department of Computer Science. Portions of these results were reported in preliminary form in [1]. , 1971 .
[46] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .
[47] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .
[48] Claus-Peter Schnorr,et al. A Lower Bound on the Number of Additions in Monotone Computations , 1976, Theor. Comput. Sci..
[49] Leonid A. Levin,et al. Average Case Complete Problems , 1986, SIAM J. Comput..
[50] Russ Bubley,et al. Randomized algorithms , 1995, CSUR.
[51] Daniel N. Osherson,et al. Thinking (vol. 3): an invitation to cognitive science , 1990 .
[52] Claude E. Shannon,et al. The synthesis of two-terminal switching circuits , 1949, Bell Syst. Tech. J..
[53] J. Büchi. Weak Second‐Order Arithmetic and Finite Automata , 1960 .
[54] Volker Strassen,et al. A Fast Monte-Carlo Test for Primality , 1977, SIAM J. Comput..
[55] Johan Håstad,et al. Almost optimal lower bounds for small depth circuits , 1986, STOC '86.
[56] Ravi Kannan,et al. Circuit-Size Lower Bounds and Non-Reducibility to Sparse Sets , 1982, Inf. Control..
[57] Michael J. Fischer,et al. Relations Among Complexity Measures , 1979, JACM.
[58] Noga Alon,et al. The monotone circuit complexity of boolean functions , 1987, Comb..
[59] Juris Hartmanis,et al. On isomorphisms and density of NP and other complete sets , 1976, STOC '76.
[60] A. K. Chandra,et al. Intrinsically Difficult Problems , 1979 .
[61] Claus-Peter Schnorr. The network complexity and the Turing machine complexity of finite functions , 2004, Acta Informatica.
[62] John Gill,et al. Relativizations of the P =? NP Question , 1975, SIAM J. Comput..
[63] Aaron D. Wyner,et al. The Synthesis of TwoTerminal Switching Circuits , 1993 .
[64] R. Solovay,et al. Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question , 1975 .
[65] Albert R. Meyer,et al. The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.
[66] Miklós Ajtai,et al. Generating hard instances of lattice problems (extended abstract) , 1996, STOC '96.
[67] John T. Gill,et al. Computational complexity of probabilistic Turing machines , 1974, STOC '74.
[68] L. H. Harper,et al. A Class of Boolean Functions with Linear Combinational Complexity , 1975, Theor. Comput. Sci..
[69] John E. Savage,et al. Computational Work and Time on Finite Machines , 1972, JACM.
[70] Bruno Scarpellini. Complex Boolean Networks Obtained by Diagonalization , 1985, Theor. Comput. Sci..
[71] Edward L. Robertson. Structure of complexity in the weak monadic second-order theories of the natural numbers , 1974, STOC '74.
[72] C. C. Elgot. Decision problems of finite automata design and related arithmetics , 1961 .
[73] Allan Borodin,et al. On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..
[74] Jeffrey D. Ullman,et al. Introduction to Automata Theory, Languages and Computation , 1979 .
[75] David Thomas,et al. The Art in Computer Programming , 2001 .
[76] Paul Young. Review: Manuel Blum, Recursive Function Theory and Speed of Computation , 1972 .
[77] R. J. Nelson,et al. Introduction to Automata , 1968 .
[78] Larry Joseph Stockmeyer,et al. The complexity of decision problems in automata theory and logic , 1974 .
[79] Rajeev Motwani,et al. Randomized Algorithms , 1995, SIGA.
[80] M. Rabin. Degree of difficulty of computing a function and a partial ordering of recursive sets , 1960 .
[81] Wolfgang J. Paul. A 2.5 n-lower bound on the combinational complexity of Boolean functions , 1975, STOC '75.
[82] Andrew Chi-Chih Yao,et al. Quantum Circuit Complexity , 1993, FOCS.
[83] Leonard M. Adleman,et al. Quantum Computability , 1997, SIAM J. Comput..
[84] Ravi B. Boppana,et al. The Complexity of Finite Functions , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.
[85] Larry J. Stockmeyer,et al. Classifying the computational complexity of problems , 1987, The Journal of Symbolic Logic.
[86] John Gill,et al. Relative to a Random Oracle A, PA != NPA != co-NPA with Probability 1 , 1981, SIAM J. Comput..